The field of graph algorithms and parameterized complexity is rapidly advancing, with significant developments in dynamic algorithms, parameterized tractability, and approximation techniques. Researchers are exploring new approaches to solve long-standing open problems, such as computing optimal tree decompositions and maintaining maximal matchings in dynamic graphs. Noteworthy papers in this area include 'Fully Dynamic Algorithms for Transitive Reduction' and 'Deterministic Dynamic Maximal Matching in Sublinear Update Time', which present innovative solutions to these problems. Another notable work is 'Boundaried Kernelization', which introduces a new model for efficient local preprocessing and establishes polynomial boundaried kernelizations for several problems.
Advances in Graph Algorithms and Parameterized Complexity
Sources
Geodetic Set on Graphs of Constant Pathwidth and Feedback Vertex Set Number
Non-distributive Lattices, Stable Matchings, and Linear Optimization
Fully Dynamic Algorithms for Transitive Reduction
Solving Partial Dominating Set and Related Problems Using Twin-Width
Treewidth Parameterized by Feedback Vertex Number
Computing Distances on Graph Associahedra is Fixed-parameter Tractable
On constrained intersection representations of graphs and digraphs
Boundaried Kernelization
Entrywise Approximate Matrix Inversion
Faster Dynamic $(\Delta+1)$-Coloring Against Adaptive Adversaries
Deterministic Dynamic Maximal Matching in Sublinear Update Time
Concurrency Constrained Scheduling with Tree-Like Constraints
Elimination Distance to Dominated Clusters